Why isn't it appropriate for an interviewee to be represented by a negotiation expert like companies do for salary talks?

You're absolutely right. It is unfair to the employee to NOT get professional representation.

Negotiation is not as easy as it seems. In 2016, one NFL player decided that it was "easy to negotiate" and tried to represent himself. The deal he self-negotiated was widely panned as one of the worst labor contracts ever:

“I think the Russell Okung contract might be the biggest debacle of a contract I have ever seen. Okung, who at this stage of his career is somewhere between the 10th and 15th-best left tackle in football, eschewed an agent, decided to negotiate his own contract, and signed with Denver for a non-guaranteed $5 million for 2016. … For a player of his stature, it’s a ridiculous contract.”

- Peter King, Sports Illustrated, March 20, 2016

On the other side, most recruiters are TOUGH negotiators. They absolutely DESTROY candidates. It's not so much that recruiters are the Navy Seals of negotiation. That is, most recruiters haven't had extensive negotiation training and their tactical (negotiation) moves are only a slight cut above the average person's.

It's more because recruiters have two MASSIVE innate (not trained) advantages that candidates don't:

Information. In addition to knowing internal compensation tables, they talk to 20-30 candidates every single day. And each one of these candidates is (usually) handing over their personal compensation details. So recruiters have a VERY ACCURATE sense of what the market is paying. Last time I checked, few, if any, candidates are asking 20-30 peers for five years straight what they're making.

Leverage. The company has the offer. If this candidate doesn't accept, there are lots of others to choose from. The candidate needs the offer (aka money to go clubbing, pay the mortgage, etc.) BADLY. And most candidates have few, if any, competing offers.

For professional athletes, actors, and singers, it's appropriate for them to have representation at salary talks because it's the norm.

For executive-level compensation or organized labor, professional representation is also the norm.

But for standard employee-to-employer negotiations, professional representation is not appropriate only because it's not commonplace. During the offer discussion stage, if you told a recruiter to "talk to my agent," they'll either mock you, get scared, or both. If you want a good negotiation outcome, last thing you want is to deal with another party that either despises you or is afraid of you.

But as Bobby Arora puts it, you can create a "synthetic situation" where you can have a simulated professional agent representing you. I'll call it a "shadow negotiator."

It would be exactly as Bobby puts it. You relay the compensation information you're hearing from the recruiter, and the shadow negotiator (behind the scenes) tells you what to say and do. Thanks to the digital age, negotiation via email is becoming more commonplace, so it'll be even easier to relay information to your shadow negotiator.